Consider a matrix \(\mathbf {X}\in \mathbb {R}^{M\times T}\)  for a time series corpus that consists of \(M\)  correlated streams with \(T\)  time steps for each stream. On one hand, there are generally three scenarios of time series anomaly detection depending on the availability of training data and anomaly labels: supervised, semi-supervised and unsupervised [1]}. Anomaly detection tasks without cleanWe use `clean' to describe time series data contain only normal patterns data or anomaly labels also referred to as unsupervised detection. Unsupervised methods have their advantages that no anomaly labels is needed, which is cost-saving, and they can enjoy better flexibility when the anomaly pattern drifts over time. On the other hand, time series anomaly detection can be in general divided into two settings: i) subsequence or whole sequence level anomaly whereby a subsequence \(\mathbf {x}_{m,t_1:t_2}\)  is labeled as an anomaly; ii) point level anomaly for which a measurement \(x_{m,t}\)  at time \(t\)  in sequence \(m\)  is treated as an anomaly. The former scenario is usually more challenging than the latter. For more comprehensive surveys, readers are referred to [2]}, [3]}, [4]}.
